Optimum modulator bias systems and methods in coherent optical transmitters

ABSTRACT

A modulator bias selection method, a coherent optical transmitter, and optical modulator solve the problem of generating a correct constellation using the bias points with the minimum phase adjustment range. The optimum modulator bias systems and methods include a coherent optical transmitter with control of four (XI, XQ, YI, YQ) quadrature data signals via a transmitter (Tx) application specific integrated circuit (ASIC), with a modulator bias controller which implements an algorithm to find the optimum bias points. The optimum bias points yield a correct constellation with minimum phase/bias adjustment. An algorithm is used to find the optimum bias solution using fast, simple method, adjusting only one quadrature at a time and exploiting a control feature of the Tx ASIC. This algorithm is significantly simpler than a generalized search, is a local algorithm, and uses only DC power measurement at the transmitter.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to optical communicationsystems and methods. More particularly, the present disclosure relatesto optimum modulator bias systems and methods in coherent opticaltransmitters.

BACKGROUND OF THE DISCLOSURE

In next generation optical modems (e.g., 100 Gb/s and beyond), and inparticular in transmitters, there is a requirement for greater opticalperformance (via better control of optical modulators) and for allowinga wider choice of vendors/technologies (i.e. different lithium niobate(LiNbO₃) modulator vendors or indium phosphide (InP) photonicintegration technologies). In particular, the new InP technology isprized for its small size and anticipated lower cost (and consequentlyis proposed to be used in next gen small-form-factor pluggable optics).One of the most important functions of transmitter control is to bias amodulator so it transmits a distortion free and correct optical dataconstellation via selecting the correct “bias points” (optical phasepoints). Conventionally, lithium niobate modulators have been used whichhave a large (optical) phase adjustment range and therefore, flexiblemodulator bias points. By flexible modulator bias points, this meansthat there is more than one set of bias points available with about thesame optical performance. Using lithium niobate modulators, ageneralized search can be implemented to find “reasonable” bias points,but these are not necessarily optimum points. That is, there is littleperformance degradation when operating at non-optimum bias points. InPtechnology has a relatively small phase adjustment range and thus, if apoor hardware scheme and algorithm for bias point selection is used, thecorrect constellation cannot be generated or unnecessary cost is addeddue to rejected modulators. Also, InP modulators have twice the phasecontrols, so for each modulator polarization, the search space is muchlarger: 6-dimensional vs. 3-dimensional (for LiNbO₃). In addition,because of InP physics, it is necessary to find the minimum phase biaspoints to get best cost and performance.

BRIEF SUMMARY OF THE DISCLOSURE

In an exemplary embodiment, a modulator bias selection method includes,for each pair of inner phase adjusters of an optical modulator,selecting a minimum bias point by sweeping a left phase adjuster and aright phase adjuster of each of the inner phase adjusters to find theminimum bias point; for each pair of outer phase adjusters, selecting ahalf-power bias point by separately sweeping a left phase adjuster and aright phase adjuster of each of the outer phase adjusters to find thehalf-power bias point; and setting the pair of inner phase adjusters andthe pair of outer phase adjusters based on the selecting steps, whereinthe modulator bias selection method includes a local algorithm. Themodulator bias selection method can further include performing theselecting steps and the setting step for each polarization, in-phase andquadrature, of the optical modulator. The modulator bias selectionmethod can further include, during the selecting the minimum bias pointstep, using any one of a plurality of detectors to find the minimum biaspoint; and, during the selecting the half-power bias point step, usingone of an inner detector of the plurality of detectors or an externaldetector of the plurality of detectors. The modulator bias selectionmethod can further include selecting the minimum bias point when a phaseof a left phase amount minus a right phase amount plus an offset phaseamount equals 0, +/−2, +/−4, . . . ; and selecting a smaller of themagnitude of the left phase amount and the right phase amount for thesetting step.

The modulator bias selection method can further include, prior to theselecting the half-power bias point step, setting a left phase adjusterand a right phase adjuster of each of the inner phase adjusters suchthat the optical modulator is biased at a maximum bias point. For theinner phase adjusters PH_L is a value of the left phase adjuster at theminimum bias point and PH_R is a value of the right phase adjuster atthe minimum bias point; wherein for the outer phase adjusters PH_PL is avalue of the left phase adjuster at the half-power bias point and PH_PRis a value of the right phase adjuster at the half-bias point; and themethod can further include, if the optical modulator is bipolarperforming the steps of: selecting values for the inner phase adjustersbased on if PH_L is smaller than PH_R and PH_L=K, then PH_L=K/2 andPH_R=−K/2, else PH_R=K/2 and PH_L=−K/2; and selecting values for theouter phase adjusters based on if PH_PL smaller than PH_PR and PH_PL=K,then PH_PL=K/2 and PH_PR=−K/2, else PH_PR=K/2, PH_PL=−K/2; and if theoptical modulator is not bipolar performing the steps of: selecting forthe inner phase adjusters values based on if PH_L is smaller than PH_Rand PH_L=K, then PH_L=K and PH_R=0, else PH_R=K and PH_L=0; andselecting for the output phase adjusters based on if PH_PL smaller thanPH_PR and PH_PL=K, then PH_PL=K and PH_PR=0, else PH_PR=K, PH_PL=0.

The modulator bias selection method can further include, depending on aslope of power versus phase in the selecting the half-power bias pointstep, selectively performing data inversion to get a desiredconstellation; wherein data inversion can include one of inverting atransfer function in a digital filter coupled to a digital input orinverting an analog amplifier gain of an analog amplifier coupled to ananalog output; wherein data inversion is selectively performed eitherfor an in-phase component or a quadrature component. The modulator biasselection method can further include selecting the minimum bias pointwhen a phase of a left phase amount minus a right phase amount plus anoffset phase amount equals 0, +/−2, +/−4, . . . ; selecting a smaller ofthe magnitude of the left phase amount and the right phase amount forthe setting step; and, if the optical modulator is bipolar, dividing thesmaller of the magnitude of the left phase amount and the right phaseamount for the setting step by two and setting the other magnitude to asame value with a negative sign. The modulator bias selection method canfurther include setting feedback controller polarity based on a slope ofpower versus phase in the selecting the half-power bias point step.Optionally, the optical modulator includes a lithium niobate opticalmodulator, an indium phosphate optical modulator, and/or a quad-parallelMach-Zehnder modulator.

In another exemplary embodiment, a coherent optical transmitter includesan optical modulator system including a plurality of modulators and aplurality of detectors monitoring outputs of the plurality ofmodulators; a modulator bias controller communicatively coupled to theplurality of detectors monitoring outputs and providing phase biascontrol to a plurality of phase adjusters associated with the pluralityof modulators; transmitter circuitry receiving a digital input andproviding an analog output to the plurality of modulators; and amodulator bias selection algorithm operating between the opticalmodulator system, the modulator bias controller, and the transmittercircuitry to select optimum phases for the plurality of phase adjustersin a local and non-iterative manner. The transmitter circuitry caninclude a digital transfer function, H, applied to the digital input; adigital to analog converter receiving an output of the digital transferfunction, H; and an analog amplifier with gain, G, receiving an outputof the digital to analog converter; wherein the plurality of modulatorscan be bipolar, and wherein the modulator bias selection algorithm canselectively performs data inversion on one of the gain, G, or thedigital transfer function, H, to get a desired constellation.

The modulator bias selection algorithm can cause the transmittercircuitry and the modulator bias controller to perform the steps of: foreach pair of inner phase adjusters of the optical modulator system,selecting a minimum bias point by sweeping a left phase adjuster and aright phase adjuster of each of the inner phase adjusters to find theminimum bias point; for each pair of outer phase adjusters of theoptical modulator system, selecting a half-power bias point byseparately sweeping a left phase adjuster and a right phase adjuster ofeach of the outer phase adjusters to find the half-power bias point; andsetting the pair of inner phase adjusters and the pair of outer phaseadjusters based on the selecting steps. The modulator bias selectionalgorithm can use any one of the plurality of detectors to find theminimum bias point during the selecting the minimum bias point step; andwherein the modulator bias selection algorithm can use one of an innerdetector of the plurality of detectors or an external detector of theplurality of detectors during the selecting the half-power bias pointstep.

For the inner phase adjusters PH_L is a value of the left phase adjusterat the minimum bias point and PH_R is a value of the right phaseadjuster at the minimum bias point; wherein for the outer phaseadjusters PH_PL is a value of the left phase adjuster at the half-powerbias point and PH_PR is a value of the right phase adjuster at thehalf-bias point; and the modulator bias selection algorithm can causethe transmitter circuitry and the modulator bias controller to performthe steps of: if the optical modulator is bipolar performing the stepsof: selecting values for the inner phase adjusters based on if PH_L issmaller than PH_R and PH_L=K, then PH_L=K/2 and PH_R=−K/2, else PH_R=K/2and PH_L=−K/2; and selecting values for the outer phase adjusters basedon if PH_PL smaller than PH_PR and PH_PL=K, then PH_PL=K/2 andPH_PR=−K/2, else PH_PR=K/2, PH_PL=−K/2; and if the optical modulator isnot bipolar performing the steps of: selecting for the inner phaseadjusters values based on if PH_L is smaller than PH_R and PH_L=K, thenPH_L=K and PH_R=0, else PH_R=K and PH_L=0; and selecting for the outputphase adjusters based on if PH_PL smaller than PH_PR and PH_PL=K, thenPH_PL=K and PH_PR=0, else PH_PR=K, PH_PL=0.

In yet another exemplary embodiment, and optical modulator includes Nphase adjustment points; M detectors associated with the N phaseadjustment points, N≧M; circuitry communicatively coupled to the N phaseadjustment points and the M detectors, wherein the circuitry isconfigured to: for each pair of inner adjustment points of the N phaseadjustment points, select a minimum bias point by sweeping a left phaseadjustment point and a right phase adjustment point of each of the inneradjustment points to find the minimum bias point where a phase of a leftphase amount minus a right phase amount plus an offset phase amountequals 0, +/−2, +/−4, . . . ; for each pair of outer phase adjustmentpoints of the N phase adjustment points, select a half-power bias pointby separately sweeping a left phase adjustment point and a phaseadjustment point of each of the outer phase adjustment points to findthe half-power bias point; and set the pair of inner phase adjustmentpoints and the pair of phase adjustment points based on the select stepsat an optimum value determined in a local and non-iterative manner. Theoptical modulator can be a quad-parallel Mach-Zehnder modulator.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is illustrated and described herein withreference to the various drawings, in which like reference numbers areused to denote like system components/method steps, as appropriate, andin which:

FIG. 1 is a block diagram of an optical modulator system with optimumbias control;

FIG. 2 is a block diagram of functional details associated with theTransmitter (Tx) ASIC in FIG. 1;

FIG. 3 is a schematic diagram illustrates details of the quad-parallelMach-Zehnder (QPMZ) modulator of FIG. 1 showing locations and naming ofphase/bias control ports;

FIG. 4 is a flowchart of a generalized modulator bias control methodwhich can be used in the optimum bias control described herein; and

FIGS. 5A and 5B are a flowchart of an optimum bias control method 80which is a local algorithm based on a set of constraints.

DETAILED DESCRIPTION OF THE DISCLOSURE

In various exemplary embodiments, the present disclosure relates tooptimum modulator bias systems and methods in coherent opticaltransmitters. The optimum modulator bias systems and methods solve theproblem of generating the correct constellation using the (bias points)with the minimum phase adjustment range. The optimum modulator biassystems and methods include a coherent optical transmitter with controlof four (XI, XQ, YI, YQ) quadrature data signals via a transmitter (Tx)application specific integrated circuit (ASIC), with a modulator biascontroller which implements an algorithm to find the optimum biaspoints. The optimum bias points yield a correct constellation withminimum phase/bias adjustment. An algorithm is used to find the optimumbias solution using fast, simple method, adjusting only one quadratureat a time and exploiting a control feature of the Tx ASIC. Thisalgorithm is significantly simpler than a generalized search, is a localalgorithm, and uses only DC power measurement at the transmitter.

Referring to FIG. 1, in an exemplary embodiment, a block diagramillustrates an optical modulator system 10 with optimum bias control.The optical modulator system 10 includes a combination of optical andelectrical components such as, for example, a quad-parallel Mach-Zehnder(QPMZ) modulator 12, a laser 14, modulator bias controller 16,transmitter (Tx) controller 18, and a Tx ASIC 20. The laser 14 iscommunicatively coupled to the modulator 12 providing a laser outputthereto which is modulated by the modulator 12. The modulator 12 is usedfor multi-value modulation methods such as N-quadrature amplitudemodulation (QAM), differential quadrature phase shift keying (DQPSK),etc. In general, when any multi-value modulation methods are use, anin-phase/quadrature (I/Q) modulator is used as the optical modulator 12.The I/Q modulator 12 is an optical modulator capable of independentlygenerating orthogonal optical electric field components (I channel and Qchannel) and has a structure in which Mach-Zehnder (MZ) modulators areconnected in parallel. For example, the QPMZ modulator 12 can also bereferred to as a dual parallel MZ modulator and can be used in a 16-QAMmodulation scheme in the optical modulator system 10. As is shown inFIG. 1, there are an increased number of modulator bias points in theQPMZ modulator 12 which need to be optimized with the optimum biascontrol.

The Tx ASIC 20 receives a digital information stream at a digital input22 and converts the digital information stream appropriately, based onan associated modulation scheme, for driving the modulator 12 via analogoutputs 24. The analog outputs 24 are communicatively coupled to themodulator 12 (labeled Radio Frequency (RF) XI, XQ, YI, YQ, where X, Ydenotes polarization and I, Q denote in-phase and quadrature,respectively). The modulator 12 includes four modulators 26, 28, 30, 32including a XI modulator 26, a XQ modulator 28, a YI modulator 30, and aYQ modulator 32. A detector 34 (also referred to as a tap-detectorinterchangeably) is included at an output of each of the modulators 26,28, 30, 32. The modulators 26, 28, 30, 32 can be referred to as innermodulators and can be either amplitude, phase, or mixed phase/amplitudemodulators. In an exemplary embodiment, the modulators 26, 28, 30, 32can be phase modulators. Additionally, the modulator 12 include anX-polarization detector 36 coupled to a combined output of themodulators 26, 28 and a Y-polarization detector 38 coupled to a combinedoutput of the modulators 30, 32. A polarization rotator 40 can beconnected to the combined output of the modulators 30, 32. Apolarization beam combiner 42 can be connected to the combined output ofthe modulators 26, 28 and the combined output of the modulators 30, 32.An output of the polarization beam combiner 42 provides a modulatedoutput of the modulator 12, and an external detector 44 can be tappedoff the output. The various detectors 34, 36, 38, 44 are communicativelycoupled to the modulator bias controller 16.

The Tx controller 18, in this exemplary embodiment, implements a“optimum bias point selection” algorithm, controls the Tx ASIC 20, andthe modulator bias controller 16. Specifically, the Tx controller 18controls the modulator bias controller 16 in the following ways: (i)open loop control: bias control loops are opened enabling direct controlof biases and measurement of the detectors 34, 36, 38, 44, (ii) closedloop control: sets the feedback polarity of the modulator biascontroller 16, but the modulator bias controller 16 itself implementsthe feedback control. The Tx controller's 18 algorithm finds the optimumbias points; the modulator bias controller 16 is responsible formaintaining those points in service.

Referring to FIG. 2, in an exemplary embodiment, a block diagramillustrates functional details associated with the Tx ASIC 20. The TxASIC 20 includes a digital filter 50 receiving the digital input 22 andincluding a transfer function, H, a digital-to-analog (D/A) converter 52connected to an output of the digital filter 50, and an analog amplifier54 connected to an output of the D/A converter 52 and including gain, G.An output of the analog amplifier 54 provides the analog output 24 tothe modulator 12. A controller 56 is connected to the digital filter 50and the analog amplifier 54 for controlling the transfer function, H,and the gain, G, responsive to a data inversion control signal 58 fromthe Tx controller 18.

Referring to FIG. 3, in an exemplary embodiment, a schematic diagramillustrates details of the QPMZ modulator showing locations and namingof phase/bias control ports. The locations and naming of phase/biascontrol ports are used in the foregoing descriptions of the optimum biascontrol. The modulator 12 includes an input 60 which is split between anX polarization 62 and a Y polarization 64. The X polarization 62 issplit again with associated phase/bias control points PH_XPL, PH_XPRwhere PH is used to denote phase, X to denote the X polarization, P todenote these are outer phase control points, and L and R for left andright to distinguish therebetween. The Y polarization 64 is split againwith associated phase/bias control points PH_YPL, PH_YPR where PH isused to denote phase, Y to denote the Y polarization, P to denote theseare outer phase control points, and L and R for left and right todistinguish therebetween. Thus, from an outer phase control perspective,there are four phase/bias control points PH_XPL, PH_XPR, PH_YPL, PH_YPR.

At an output of the phase/bias control point PH_XPR, there are twoadditional phase/bias control points PH_XIL, PH_XIR where PH is used todenote phase, X to denote the X polarization, I to denote in-phase, andL and R for left and right to distinguish therebetween. At an output ofthe phase/bias control point PH_XPL, there are two additional phase/biascontrol points PH_XQL, PH_XQR where PH is used to denote phase, X todenote the X polarization, Q to denote quadrature, and L and R for leftand right to distinguish therebetween. At an output of the phase/biascontrol point PH_YPR, there are two additional phase/bias control pointsPH_YIL, PH_YIR where PH is used to denote phase, Y to denote the Ypolarization, I to denote in-phase, and L and R for left and right todistinguish therebetween. At an output of the phase/bias control pointPH_YPL, there are two additional phase/bias control points PH_YQL,PH_YQR where PH is used to denote phase, Y to denote the Y polarization,Q to denote quadrature, and L and R for left and right to distinguishtherebetween.

The problem statement of the optimum bias control is as follows. Theoptical electric field at the output of the transmitter can be describedby: (for one polarization)

E=E _(I) ·e ^((jπ(PH) ^(—) ^(PR+PHOffset) ^(—) ^(P)))+E _(Q) ·e^((jπ(PH) ^(—) ^(PL))

where:

$E_{I} = {A_{I} \cdot ^{({j\frac{\pi}{2}{({{PH\_ IL} + {PH\_ IR} + {{PHOffset\_}I}})}})} \cdot {\sin \left( {\frac{\pi}{2}{V\_ I}} \right)} \cdot {\cos \left( {\frac{\pi}{2}{M\_ I}} \right)}}$$E_{Q} = {A_{Q} \cdot ^{({j\frac{\pi}{2}{({{PH\_ QL} + {PH\_ QR} + {{PHOffset\_}Q}})}})} \cdot {\sin \left( {\frac{\pi}{2}{V\_ Q}} \right)} \cdot {\cos \left( {\frac{\pi}{2}{M\_ Q}} \right)}}$A_(I) = [−1, 1], A_(Q) = [−1, 1], selectable.

For the optimum bias control, one must find the set of minimum PH_IL,PH_IR, PH_QL, PH_QR, PH_PL, PH_PR for any given PHOffset_I, PHOffset_Q,PHOffset_P;

With constraints of: PH_IL−PH_IR+PHOffset_I=M_I=0, +/−2, +/4 . . . ,PH_QL−PH_QR+PHOffset_Q=M_Q=0, +/−2, +/4 . . . ;

Given the freedom to select A_I/A_Q, . . . ;

Such that:

$E = {{\sin \left( {\frac{\pi}{2}{V\_ I}} \right)} + {^{j\frac{\pi}{2}} \cdot {\sin \left( {\frac{\pi}{2}{V\_ Q}} \right)}}}$

provides the desired correct data constellation.

Conventionally, lithium niobate modulators are used which have (nearly)no restriction on the magnitude of PH_IL, PH_IR, PH_QL, PH_QR, PH_PL,PH_PR, so finding the desired correct data constellation was easy. Thenew InP technology has a relatively small phase adjustment range (limitson PH_IL, etc.). The physics of phase adjustment in InP (viafree-carrier, thermal, Stark effect mechanisms) is much weaker than thelinear electro-optic effect in lithium niobate. Furthermore, the phasecontrols are nonlinear, saturating, and accompanied by opticalabsorption (unlike lithium niobate). The latter is especiallyproblematic, the optical absorption increases as the phase adjustmentincreases, degrading the extinction ratio in the modulator, andincreasing the constellation distortion which hurts the transmitteroptical performance.

Referring to FIG. 4, in an exemplary embodiment, a flowchart illustratesa generalized modulator bias control method 70 which can be used in theoptimum bias control described herein. The generalized modulator biascontrol method 70 includes measuring a control metric at detectors/tapsby dithering modulator phase control and measuring optical power ditherat detectors (step 72). This can be done via the various detectors 34,36, 38, 44. The generalized modulator bias control method 70 alsoincludes applying correct feedback polarity (+/−1) based on the on theset of bias points (I, Q, P) (step 74). Finally, the generalizedmodulator bias control method 70 includes calculating a new modulator(phase) bias setting (step 76). For example, a description coveringmodulator bias control methods is included in commonly assigned U.S.Patent Publ. No. 2010/0272446 entitled “CONTROL SYSTEM FOR A POLAROPTICAL TRANSMITTER,” the contents of which are incorporated byreference herein.

With respect to modulator bias nomenclature: “Min”, “Max”, “Quad”/“Halfpower” bias points, the optical electric field for one interferometer,say I: (and for one polarization) is:

$E_{I} = {A_{I} \cdot ^{({j\frac{\pi}{2}{({{PH\_ IL} + {PH\_ IR} + {{PHOffset\_}I}})}})} \cdot {\sin \left( {\frac{\pi}{2}{V\_ I}} \right)} \cdot {\cos \left( {\frac{\pi}{2}{M\_ I}} \right)}}$

where PH_IL−PH_IR+PHOffset_I=M_I=0, +/−2, +/4, . . . . This equation wasderived as follows:

$\begin{matrix}{\mspace{79mu} {{E_{I} = {^{({j\frac{\pi}{2}{({V + {2{PH\_ L}} + {2{PHOffset}}})}})} - ^{({j\frac{\pi}{2}{({{- V} + {2{PH\_ R}}})}})}}}{E_{I} = {^{({j\frac{\pi}{2}{({{PH\_ L} + {PH\_ R} + {PHOffset}})}})} \cdot \begin{bmatrix}{^{({j\frac{\pi}{2}{({V + {PH}_{L} - {PH}_{R} + {PHOffset}})}})} -} \\^{({j\frac{\pi}{2}{({{- V} - {PH}_{L} + {PH}_{R} - {PHOffset}})}})}\end{bmatrix}}}}} & {{Eq}.\mspace{14mu} (1)}\end{matrix}$

$\mspace{79mu} {E_{I} = {^{({j\frac{\pi}{2}{({{PH\_ L} + {PH\_ R} + {PHOffset}})}})} \cdot \begin{bmatrix}{^{({j\frac{\pi}{2}{({V + {PH}_{L} - {PH}_{R} + {PHOffset}})}})} -} \\^{({{- j}\frac{\pi}{2}{({V + {PH}_{L} - {PH}_{R} + {PHOffset}})}})}\end{bmatrix}}}$${E_{I} = {^{({j\frac{\pi}{2}{({{PH\_ L} + {PH\_ R} + {PHOffset}})}})} \cdot {\sin \left( {\frac{\pi}{2}\left( {V + {PH\_ L} - {PH\_ R} + {PHOffset}} \right)} \right)}}},$

where PHOffset=[−1:1] and is a random manufacturing phase.

${E_{I} = {{^{({j\frac{\pi}{2}{({{PH\_ L} + {PH\_ R} + {PHOffset}})}})} \cdot {\sin \left( {\frac{\pi}{2}V} \right)}}{\cos \left( {\frac{\pi}{2}\left( {{PH\_ L} - {PH\_ R} + {PHOffset}} \right)} \right)}}},$

where PH_L−PH_R+PHOffset=0, +/−2, +/4 . . . are possible bias points.

Starting from the original equation, Eq. (1):

$E_{I} = {^{({j\frac{\pi}{2}{({V + {2{PH\_ L}} + {2{PHOffset}}})}})} - ^{({j\frac{\pi}{2}{({{- V} + {2{PH\_ R}}})}})}}$

The following assumptions can be made to simplify the mathematics:PH_R=−PH_L=−PH/2, PHOffset=0, thereby simplifying the Eq. (1) asfollows:

$E_{I} = {{^{({j\frac{\pi}{2}{({V + {PH}})}})} - ^{({j\frac{\pi}{2}{({{- V} - {PH}})}})}} = {2{j \cdot {\sin \left( {\frac{\pi}{2} \cdot \left( {V + {PH}} \right)} \right)}}}}$

which results in the measured optical power of:

$P = {{4 \cdot \left\lbrack {\sin \left( {\frac{\pi}{2} \cdot \left( {V + {PH}} \right)} \right)} \right\rbrack^{2}} = {2 \cdot \left( {1 - {\cos \left( {\pi \cdot \left( {V + {PH}} \right)} \right)}} \right)}}$

which, assuming “DC”, i.e. V=0 (no RF modulation) and normalizing,becomes

P=½·(1−cos(π·PH))

Therefore, a minimum “min” bias point is when PH=0, P=0, i.e. theminimum DC optical power; a maximum “max” bias point is when PH=1, P=1,i.e. the maximum DC optical power; and a quadrature “Quad” or “halfpower” bias point is when PH=0.5, P=0.5, i.e. the half-power point.

Referring to FIGS. 5A-5B, in an exemplary embodiment, a flowchartillustrates an optimum bias control method 80 based on the foregoing.Specifically, the optimum bias control method 80 utilizes theaforementioned “min” bias point, “max” bias point, and “half power” biaspoint to implement a local algorithm to find optimal bias settings forPH_XPR, PH_XPL, PH_YPR, PH_YPL, PH_XIR, PH_XIL, PH_XQR, PH_XQL, PH_YIR,PH_YIL, PH_YQR, and PH_YQL. Starting in FIG. 5A, the optimum biascontrol method 80 is performed for each polarization (A_I=1, A_Q=1)(step 81). The optimum bias control method 80 includes, for each pair ofinner phase adjusters, selecting the “min”, i.e. findPH_L−PH_R+PHOffset=M=0, +/−2, +/−4, by sweeping PH_L and PH_R separatelyto find the first minimum power point; select the smaller magnitude ofPH_L, PH_R. Do this twice; for I and Q inner modulators (step 82). Thestep 82 can use any of the detectors 34, 36, 40, 44.

The optimum bias control method 80 can include a physical mechanismwhich allows PH_X (X=L or R) to be bipolar (i.e. PH_X can be positive ornegative) (step 83). If the physical mechanism PH_X cannot be bipolar(step 83), if PH_L is smaller than PH_R (and PH_L=K) PH_L=K, PH_R=0,else PH_R=K, PH_L=0 (step 84). If the physical mechanism PH_X can bebipolar (step 83), if PH_L is smaller than PH_L (and PH_L=K), PH_L=K/2,PH_R=−K/2; else PH_R=K/2, PH_L=−K/2 (step 85). The steps 84, 85 yieldthe optimum settings of PH_L and PH_R and are remembered for later inthe optimum bias control method 80 (step 86). The optimum bias controlmethod 80, in general, could sweep differentially, but specifically toInP there is no advantage because none of the three common physicalmechanisms for varying the phase (PH_L etc.) are bipolar, i.e. the phasecontrol cannot change sign, only increase or decrease in magnitude(unlike lithium niobate). As an aside, in the case of Lithium Niobatemodulators, the optimum bias control method 80 works equally well, butusually because of device physics PH_L=−PH_R and there is only one phasecontrol that applies the phase differentially.

The optimum bias control method 80 includes a preparatory step of, forboth the I and Q inner modulators, setting PH_L or PH_R or both so themodulator is biased at the “max” bias point (step 87). The optimum biascontrol method 80 next includes, for each pair of outer phase adjusters,selecting the “quad” bias point, by sweeping PH_PL and PH_PR separatelyto find the first “half-power” bias point; and selecting the smallermagnitude of PH_PL, PH_PR (step 88). The step 88 can only use Inner(X-Inner or Y-Inner) or Z detectors, i.e. the detectors 36, 40, 44.Next, the optimum bias control method 80 at step 90 proceeds to FIG. 5B.

In FIG. 5B, again, the optimum bias control method 80 can include aphysical mechanism which allows PH_X (X=L or R) to be bipolar (i.e. PH_Xcan be positive or negative) (step 91). If the physical mechanism PH_Xcannot be bipolar (step 91), if PH_PL is smaller than PH_PR (andPH_PL=K), the PH_PL=K, PH_PR=0, else PH_PR=K, PH_PL=0 (step 92). If thephysical mechanism PH_X can be bipolar (step 91), if PH_PL is smallerthan PH_PR (and PH_PL=K), then PH_PL=K/2, PH_PR=−K/2, else PH_PR=K/2,PH_PL=−K/2 (step 93). The values of PH_PL and PH_PR are set (step 94).Depending on the slope of power vs. PH_P found in steps 88, 92, 93,either perform inversion to get the desired constellation or do nothing(step 95). Inversion is performed via the data inversion control 58 andincludes setting in the Tx ASIC 20 H→−H or G→−G. This is done for I orQ, but not both (i.e. A_I→−A_I or A_Q→−A_Q). Subsequent to the step 95,the optimum bias control method 80, depending on the slope of power vs.PH_P found in steps 88, 92, 93, sets the bias loops' (I, Q, P) feedbackcontroller polarity (step 96). Finally, the optimum bias control method80 resets PH_L/R to their optimum values in step 86 for both the I and Qinner modulators (step 97).

The optimum bias control method 80 can be implemented in the opticalmodulator system 10 providing a coherent optical transmitter withoptimum modulator bias selection, a coherent optical transmitter with TxASIC signal processing and a generalized QPMZ modulator, in conjunctionwith, a method to select the correct bias points of the opticalmodulator using the least phase adjustment range possible, enabling manytypes of optical modulators to be used and with better performance.Advantageously, the systems and methods maximize the performance of theoptical modem and allow a wider choice of vendors/technologies [i.e.different lithium niobate modulator vendors; InP photonic integrationtechnologies]. In particular, the new InP technology is prized for itssmall size and anticipated lower cost (and consequently is proposed tobe used in next gen small-form-factor pluggable optics). Furthermore,the optimum bias control method 80 provides an efficient and localalgorithm to find the 12 particular bias points in the QPMZ modulator 12with particular constraints and applying a minimum amount of control.Advantageously, the optimum bias control method 80 is a local algorithmin that it does not require an iterative analysis of a set of parameter;rather they are set one at a time. The optimum bias control method 80can be implemented at startup to find the optimal bias points.

In an exemplary embodiment, the optimum bias control method 80 can beimplemented in an InP modulator such as the QPMZ modulator 12 or thelike. In the lithium niobate case, typically, the inner control points(e.g., PH_XIR, PH_XIL, PH_XQR, PH_XQL, PH_YIR, PH_YIL, PH_YQR, andPH_YQL) are biased at a first NULL, of the correct polarity, closest tozero voltage (and the polarity alternates for adjacent nulls). Theoptimum bias control method 80 breaks the constraint of requiring aspecific polarity (thus the use of data inversion as a part of theoptimum bias control method 80). In the systems and methods describedherein, the InP modulator would bias at the first null; polarity isignored, and in fact does not have the same meaning Generally withrespect to phase control: InP modulators are biased as “separate” phasecontrols (e.g. PH_L and PH_R are separate and independent) whereaslithium niobate modulators are typically biased as push-pull(PH_L=−PH_R). This means that finding the optimum set of bias pointsdoes have more degrees of freedom to search with InP.

An exemplary benefit of the systems and methods described herein is itis a local search (i.e., optimize separately and sequentially I, Q,P/outer; no iterations back to I) and exploiting one extra degree offreedom (i.e., data inversion). Further, the systems and methods aremore efficient than other types of searches which could be used such asa generalized search (e.g. for a 40/100G lithium niobate based system,sweep I, Q, P . . . 3D sweep and select) or an iterative search (lithiumniobate), i.e. choose {I nearest, Q nearest, P nearest}; swap I tosecond nearest, is I or P improved? etc. Along with data inversion, thiscan give an optimum result—generalized search with data inversion (e.g.sweep I, Q, P+data inversion . . . 3D+1 sweep and select) and iterativesearch, i.e. choose {I nearest, Q nearest, P nearest}; swap I to nearestopposite polarity (if closer), invert data, is I or P improved? etc.

It will be appreciated that some exemplary embodiments described hereinmay include one or more generic or specialized processors (“one or moreprocessors”) such as microprocessors, digital signal processors,customized processors, and field programmable gate arrays (FPGAs) andunique stored program instructions (including both software andfirmware) that control the one or more processors to implement, inconjunction with certain non-processor circuits, some, most, or all ofthe functions of the methods and/or systems described herein.Alternatively, some or all functions may be implemented by a statemachine that has no stored program instructions, or in one or moreapplication specific integrated circuits (ASICs), in which each functionor some combinations of certain of the functions are implemented ascustom logic. Of course, a combination of the aforementioned approachesmay be used. Moreover, some exemplary embodiments may be implemented asa non-transitory computer-readable storage medium having computerreadable code stored thereon for programming a computer, server,appliance, device, etc. each of which may include a processor to performmethods as described and claimed herein. Examples of suchcomputer-readable storage mediums include, but are not limited to, ahard disk, an optical storage device, a magnetic storage device, a ROM(Read Only Memory), a PROM (Programmable Read Only Memory), an EPROM(Erasable Programmable Read Only Memory), an EEPROM (ElectricallyErasable Programmable Read Only Memory), Flash memory, and the like.When stored in the non-transitory computer readable medium, software caninclude instructions executable by a processor that, in response to suchexecution, cause a processor or any other circuitry to perform a set ofoperations, steps, methods, processes, algorithms, etc.

Although the present disclosure has been illustrated and describedherein with reference to preferred embodiments and specific examplesthereof, it will be readily apparent to those of ordinary skill in theart that other embodiments and examples may perform similar functionsand/or achieve like results. All such equivalent embodiments andexamples are within the spirit and scope of the present disclosure, arecontemplated thereby, and are intended to be covered by the followingclaims.

What is claimed is:
 1. A modulator bias selection method, comprising:for each pair of inner phase adjusters of an optical modulator,selecting a minimum bias point by sweeping a left phase adjuster and aright phase adjuster of each of the inner phase adjusters to find theminimum bias point; for each pair of outer phase adjusters, selecting ahalf-power bias point by separately sweeping a left phase adjuster and aright phase adjuster of each of the outer phase adjusters to find thehalf-power bias point; and setting the pair of inner phase adjusters andthe pair of outer phase adjusters based on the selecting steps, whereinthe modulator bias selection method comprises a local algorithm.
 2. Themodulator bias selection method of claim 1, further comprising:performing the selecting steps and the setting step for eachpolarization, in-phase and quadrature, of the optical modulator.
 3. Themodulator bias selection method of claim 1, further comprising: duringthe selecting the minimum bias point step, using any one of a pluralityof detectors to find the minimum bias point; and during the selectingthe half-power bias point step, using one of an inner detector of theplurality of detectors or an external detector of the plurality ofdetectors.
 4. The modulator bias selection method of claim 1, furthercomprising: selecting the minimum bias point when a phase of a leftphase amount minus a right phase amount plus an offset phase amountequals 0, +/−2, +/−4, . . . ; and selecting a smaller of the magnitudeof the left phase amount and the right phase amount for the settingstep.
 5. The modulator bias selection method of claim 1, furthercomprising: prior to the selecting the half-power bias point step,setting the a left phase adjuster and a right phase adjuster of each ofthe inner phase adjusters such that the optical modulator is biased at amaximum bias point.
 6. The modulator bias selection method of claim 1,wherein for the inner phase adjusters PH_L is a value of the left phaseadjuster at the minimum bias point and PH_R is a value of the rightphase adjuster at the minimum bias point; wherein for the outer phaseadjusters PH_PL is a value of the left phase adjuster at the half-powerbias point and PH_PR is a value of the right phase adjuster at thehalf-bias point; and the method further comprising: if the opticalmodulator is bipolar performing the steps of: selecting values for theinner phase adjusters based on if PH_L is smaller than PH_R and PH_L=K,then PH_L=K/2 and PH_R=−K/2, else PH_R=K/2 and PH_L=−K/2; and selectingvalues for the outer phase adjusters based on if PH_PL smaller thanPH_PR and PH_PL=K, then PH_PL=K/2 and PH_PR=−K/2, else PH_PR=K/2,PH_PL=−K/2; and if the optical modulator is not bipolar performing thesteps of: selecting for the inner phase adjusters values based on ifPH_L is smaller than PH_R and PH_L=K, then PH_L=K and PH_R=0, elsePH_R=K and PH_L=0; and selecting for the output phase adjusters based onif PH_PL smaller than PH_PR and PH_PL=K, then PH_PL=K and PH_PR=0, elsePH_PR=K, PH_PL=0.
 7. The modulator bias selection method of claim 1,further comprising: depending on a slope of power versus phase in theselecting the half-power bias point step, selectively performing datainversion to get a desired constellation; wherein data inversioncomprises one of inverting a transfer function in a digital filtercoupled to a digital input or inverting an analog amplifier gain of ananalog amplifier coupled to an analog output.
 8. The modulator biasselection method of claim 7, wherein data inversion is selectivelyperformed either for an in-phase component or a quadrature component. 9.The modulator bias selection method of claim 6, further comprising:selecting the minimum bias point when a phase of a left phase amountminus a right phase amount plus an offset phase amount equals 0, +/−2,+/−4, . . . ; selecting a smaller of the magnitude of the left phaseamount and the right phase amount for the setting step; and if theoptical modulator is bipolar, dividing the smaller of the magnitude ofthe left phase amount and the right phase amount for the setting step bytwo and setting the other magnitude to a same value with a negativesign.
 10. The modulator bias selection method of claim 1, furthercomprising: setting feedback controller polarity based on a slope ofpower versus phase in the selecting the half-power bias point step. 11.The modulator bias selection method of claim 1, wherein the opticalmodulator comprises a lithium niobate optical modulator.
 12. Themodulator bias selection method of claim 1, wherein the opticalmodulator comprises an indium phosphate optical modulator.
 13. Themodulator bias selection method of claim 1, wherein the opticalmodulator comprises a quad-parallel Mach-Zehnder modulator.
 14. Acoherent optical transmitter, comprising: an optical modulator systemcomprising a plurality of modulators and a plurality of detectorsmonitoring outputs of the plurality of modulators; a modulator biascontroller communicatively coupled to the plurality of detectorsmonitoring outputs and providing phase bias control to a plurality ofphase adjusters associated with the plurality of modulators; transmittercircuitry receiving a digital input and providing an analog output tothe plurality of modulators; and a modulator bias selection algorithmoperating between the optical modulator system, the modulator biascontroller, and the transmitter circuitry to select optimum phases forthe plurality of phase adjusters in a local and non-iterative manner.15. The coherent optical transmitter of claim 14, wherein thetransmitter circuitry comprises: a digital transfer function, H, appliedto the digital input; a digital to analog converter receiving an outputof the digital transfer function, H; and an analog amplifier with gain,G, receiving an output of the digital to analog converter; wherein theplurality of modulators are bipolar, and wherein the modulator biasselection algorithm selectively performs data inversion on one of thegain, G, or the digital transfer function, H, to get a desiredconstellation.
 16. The coherent optical transmitter of claim 14, whereinthe modulator bias selection algorithm causes the transmitter circuitryand the modulator bias controller to perform the steps of: for each pairof inner phase adjusters of the optical modulator system, selecting aminimum bias point by sweeping a left phase adjuster and a right phaseadjuster of each of the inner phase adjusters to find the minimum biaspoint; for each pair of outer phase adjusters of the optical modulatorsystem, selecting a half-power bias point by separately sweeping a leftphase adjuster and a right phase adjuster of each of the outer phaseadjusters to find the half-power bias point; and setting the pair ofinner phase adjusters and the pair of outer phase adjusters based on theselecting steps.
 17. The coherent optical transmitter of claim 16,wherein the modulator bias selection algorithm uses any one of theplurality of detectors to find the minimum bias point during theselecting the minimum bias point step; and wherein the modulator biasselection algorithm uses one of an inner detector of the plurality ofdetectors or an external detector of the plurality of detectors duringthe selecting the half-power bias point step.
 18. The coherent opticaltransmitter of claim 16, wherein for the inner phase adjusters PH_L is avalue of the left phase adjuster at the minimum bias point and PH_R is avalue of the right phase adjuster at the minimum bias point; wherein forthe outer phase adjusters PH_PL is a value of the left phase adjuster atthe half-power bias point and PH_PR is a value of the right phaseadjuster at the half-bias point; and the modulator bias selectionalgorithm causes the transmitter circuitry and the modulator biascontroller to perform the steps of: if the optical modulator is bipolarperforming the steps of: selecting values for the inner phase adjustersbased on if PH_L is smaller than PH_R and PH_L=K, then PH_L=K/2 andPH_R=−K/2, else PH_R=K/2 and PH_L=−K/2; and selecting values for theouter phase adjusters based on if PH_PL smaller than PH_PR and PH_PL=K,then PH_PL=K/2 and PH_PR=−K/2, else PH_PR=K/2, PH_PL=−K/2; and if theoptical modulator is not bipolar performing the steps of: selecting forthe inner phase adjusters values based on if PH_L is smaller than PH_Rand PH_L=K, then PH_L=K and PH_R=0, else PH_R=K and PH_L=0; andselecting for the output phase adjusters based on if PH_PL smaller thanPH_PR and PH_PL=K, then PH_PL=K and PH_PR=0, else PH_PR=K, PH_PL=0. 19.An optical modulator, comprising: N phase adjustment points; M detectorsassociated with the N phase adjustment points, N≧M; circuitrycommunicatively coupled to the N phase adjustment points and the Mdetectors, wherein the circuitry is configured to: for each pair ofinner adjustment points of the N phase adjustment points, select aminimum bias point by sweeping a left phase adjustment point and a rightphase adjustment point of each of the inner adjustment points to findthe minimum bias point where a phase of a left phase amount minus aright phase amount plus an offset phase amount equals 0, +/−2, +/−4, . .. ; for each pair of outer phase adjustment points of the N phaseadjustment points, select a half-power bias point by separately sweepinga left phase adjustment point and a phase adjustment point of each ofthe outer phase adjustment points to find the half-power bias point; andset the pair of inner phase adjustment points and the pair of phaseadjustment points based on the select steps at an optimum valuedetermined in a local and non-iterative manner.
 20. The opticalmodulator of claim 19, wherein the optical modulator is a quad-parallelMach-Zehnder modulator.